Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$

We investigate the production of (longitudinal) $Z$-boson pairs in gluon fusion as a probe of anomalous Higgs couplings. Of particular interest is the kinematic region of large center-of-mass energy, where the Higgs-boson is highly off-shell. We employ the electroweak chiral Lagrangian with a light Higgs, which is the most natural effective field theory (EFT) for this process. We demonstrate this by a detailed analysis of the leading and next-to-leading EFT contributions to the amplitude, at leading order in QCD, emphasizing the role of power counting for a systematic application of the EFT. We show that at leading order the new-physics contributions are described by only two parameters, which depend on three EFT couplings. Subleading effects can be expected to be small within the range of validity of the EFT. Phenomenological implications are briefly discussed.